Isabelle Huppert (right) ‘seems to be having an absolute ball’. With Chloë Grace Moretz in Greta.
Photograph: Allstar/Focus Features

The catalyst in Neil Jordan’s thriller is a green handbag. An expensive-looking leather satchel, square with a gold clasp. Left unattended on a subway seat, it’s either an invitation or a ticking bomb (in a way, it’s both). Twentysomething Frances (Chloë Grace Moretz), heading home from her waitressing job at a fancy Manhattan restaurant, picks it up, intending to hand it in to the station’s Lost and Found, but no one is there to receive it. Reluctantly, she opens the bag, discovering a driver’s licence (with an address!) belonging to a Greta Hideg, and so to Brooklyn she goes. The French-accented Greta (Isabelle Huppert) is touched by this gesture of kindness, and insists on showing her appreciation.

Vulnerable after the death of her mother, and new to New York, having recently moved from the more navigable Boston, Frances is in the market for a new friend. And so the two become unlikely companions, making risotto and bonding over being lonely in an unfriendly city. “I’m like chewing gum: I tend to stick around,” she assures Greta, with a genuine smile.

Soon, though, both the audience and the guileless Frances will realise that Greta’s intentions are more sinister. About 30 minutes into the film, Frances happens upon a disturbing collection of items in one of Greta’s cupboards. Horrified, she confronts her, voice shaking, before walking out of the house unscathed. (This much and more is revealed in the trailer, for the spoiler-averse.)

Where can this film go for its remaining hour? I wondered, feeling as though the tension had snapped too early. Not so; its mild first act is simply Neil Jordan cracking his knuckles. The film plays out as an increasingly paranoid psychological horror, predictable in template but mostly effective in execution. Greta leaves Frances hundreds of missed calls, waiting outside her workplace for hours on end and even threatening her. “If you don’t call me, I don’t know what I will do,” declares her menacing voicemail message. In one clever chase sequence, Greta’s proximity is communicated through a terrifying series of texted photos.

It’s possible to read the film as a satire about the ineffectiveness of the New York Police Department; a rebuke to the idea that post-#MeToo it’s easier for women to report incidents of sexual harassment, stalking and related crimes. A canny millennial like Frances knows to ring the police immediately, going down to the station to file the beginnings of a restraining order. “It’s not harassment if it’s in a public place,” the officer concludes. A young woman’s safety is her problem, not the state’s.

On the other hand, maybe it’s easier to appreciate the film as pure genre. Extreme closeups of the actors ratchet up the drama; to prove exactly how unhinged Greta is, Jordan has Huppert spit chewing gum on to Moretz’s hair. At one point, Huppert has to be physically restrained. “The crazier they are, the harder they cling!” deadpans friend and roommate Erica (Maika Monroe, from It Follows, under-used but providing spiky comedy).

The film is slyly funny. “How’s the wine?” asks Frances, forced to serve her stalker at her workplace. “Like you, it promises a lot and then disappoints,” Greta growls.

Huppert seems to be having an absolute ball, pirouetting about barefoot, donning a pair of creepy leather gloves and playing Franz Liszt’s Liebesträume (Dreams of Love) on the piano (a wink, maybe, to her role in Michael Haneke’s The Piano Teacher). The blank eyes, the tight smile, the small jerking shoulders, the pinched one-liners; Greta is thin on the page but Huppert’s physical strangeness helps to animate her.

Body Double, Fatal Attraction, Single White Female, Basic Instinct – Jordan takes his cues from the stalker thrillers of the 1980s and early 1990s. Brian De Palma seems like a particular point of reference, with Jordan borrowing his canted angles and vertiginous strings in order to emphasise the woozy loss of balance in Frances’s judgment. Yet those movies revealed male anxieties about working women. Here, the characters feel too underdeveloped for the film to feel like anything more than a genre exercise; a fun and zesty throwback, sure, but strangely neutered.

Mostly, though, as a B-movie, Greta works; the moments in which it leans into its own silliness are its best. Set in New York but shot in Dublin and Toronto, the fakeness of the setting underlines the film’s campness. Admittedly, Jordan could go further. A spurting finger and, later, a syringe are deployed to hilarious, gory perfection and are the moments in which the movie pops. Jordan knows what he’s doing; the goofiness is a feature, not a bug.